3.1.

Endoscope Optics

The endoscope probe section is designed as a rigid, unit magnification, optical relay to reimage in vivo tissue to the handle optics for magnified visualization. Several rigid endoscope designs were considered for this application, and a gradient index (GRIN) probe design was chosen to reduce the number of optical elements to minimize back reflection with common path lillumination.^29–33 The endoscope probe consists of three GRIN optical elements and two optical windows. GRIN optics are specified by their pitch parameter, which relates to the number of full sinusoidal periods of the light within the rod. The selected GRIN elements were obtained from GoFoton and have a pitch of 2 for the relay rod and 0.25 for the lenses.³⁴ The two pitch relay optic was selected to accommodate the 250-mm minimum laparoscopic probe requirement since this optic has a length of 281.4 mm. The two GRIN lenses started with a 0.25-design that is designed to collimate the light from a point source. The lengths of the lenses were fabricated to accommodate the glass windows used in the system. The imaging lens has a length of 5.78 mm (0.204 pitch) to account for the 0.8-mm-thick N-BK7 window (3 mm diameter) used to provide separation between the GRIN lens and the patient. The coupling lens has a length of 5.72 mm (0.202 pitch), so the final image forms outside the 0.8-mm AR-coated window surface, leading an in-contact imaging approach with a working distance of 0. All three GRIN components have a diameter of 2.7 mm while the windows are 3 mm in diameter. These elements are shown in Fig. 1 and are labeled as follows from distal tip to proximal end: imaging lens (GoFoton ILW-2.70), relay lens (GoFoton SLR-2.70), and coupling lens (GoFoton ILW-2.70).

Fig. 1

Schematic of the endoscopic probe composed of GRIN lenses. Grin components have diameters of 2.7 mm, and the windows have a diameter of 3.0 mm. The theoretical optical path from an object placed in contact with the imaging lens, being relayed through the GRIN rod, and exiting to form an image outside the window on the coupling lens side is shown.

The components of the endoscope probe were assembled using EpoTek 301 epoxy with a refractive index of $n=1.519$, which provides a good index match for the optical components.³⁵ EpoTek 301 is a nontoxic epoxy conforming with ISO 10993 biocompatibility testing requirements and was selected due to its good optical properties and ability to withstand sterilization procedures in hydrogen peroxide gas plasma systems.³⁶ The clarity of the epoxy was verified through a series of sterilization runs on epoxy droplets placed between glass slides and GRIN lens components. The GRIN assembly of the endoscope probe is secured in an 11-gauge stainless steel hypodermic tube (MicroGroup). The hypodermic tube assists with GRIN rigidity and increases the outer diameter of the GRIN section to 3.05 mm, matching that of the window segments for better centering while placing the window components. The full window and GRIN assembly is then epoxied into a 9-gauge hypodermic tube, giving the probe a final outer diameter of 3.8 mm. The fully assembled probe is mounted onto an aluminum clamp and the threaded retaining section, as shown in Fig. 2.

Fig. 2

SolidWorks rendering of the endoscope assembly indicating the endoscope probe, fabricated clamp, and threaded retainer. The threaded retainer is threaded to match the 30 mm cage mounted components. This allows for quick connection to the handle section.

The GRIN lens parameters chosen for the design are not available in the optical design program lens database, so a full comprehensive optical software model has not been realized. The finalized design of the system made use of standard GRIN equations and theory combined with paraxial modeling using Gaussian beam parameters and ABCD matrices for on-axis light.³⁷

3.2.

Handle Optics

The handheld elements are composed of standard 30-mm-width cage mounted components from ThorLabs.³⁸ The preliminary design of the handle started with a simplified version of the benchtop model.²⁵ Weight was minimized by a selective choice of components, while keeping pupil matching requirements. An optical model of the simplified system configuration is shown in Fig. 3. This initial model allowed for the miniaturization of the benchtop system and determination of the geometrical optics parameters for the system.

Fig. 3

ZEMAX schematic of the handle layout. The surface (solid blue) and depth (dashed green) images in the inset are shown to originate from on-axis positions in the object and are then displaced by the holographic element to fill two regions on the camera as indicated by text in at the camera plane. Spacing of the lens elements are provided in the dashed brackets.

The endoscope probe relays the image of the object to the focal plane of the microscope objective. The objective is an Olympus ULWD MSPlan $50\times$ with $\mathrm{NA}=0.55$ and a focal length of 3.6 mm. The desired magnification was chosen such that the Nyquist criterion is met, i.e., more than 2 pixels are used per resolvable point in object space. The camera is a Thorlabs DCC3240N with a $1280\times 1024\mathrm{pixel}$ array of $5.3\mu \mathrm{m}$ square pixels.³⁸ To provide a system that will meet the Nyquist criterion while allowing for image degradation from aberrations, the smallest feature on a high resolution bar target with a width of $0.78\mu \mathrm{m}$ ($1.55\mu \mathrm{m}$ per line pair) is used to set the magnification. For the system to satisfy the Nyquist criterion, the $0.78\mu \mathrm{m}$ line in object space will need to take 2 pixels on the camera ($10.6\mu \mathrm{m}$) and a magnification of $10.6/0.78=13.59$. Since the focal length of the high NA objective lens is fixed, the camera lens is chosen through back calculation of the magnification equation, $|f_{\text{camera}}|=|m*f_{\text{objective}}|$, giving a camera lens focal length of 48.92 mm. A focal length of 50 mm was selected since it is a more common lens focal length and resulted in a system magnification of 13.9.

Light exiting the microscope objective enters a symmetric afocal relay of achromatic doublets (Thorlabs AC254-075-A, AC254-100-A). The relay was configured for 1:1 imaging to image the pupil of the microscope objective at the hologram plane, which allows the hologram to be the limiting aperture of the system and reduces beam overfill issues.¹⁸

The holograms used in the VHI system must provide high diffraction efficiency in a single diffraction order with high angular and wavelength selectivity. These characteristics can be achieved using volume holograms.^39,40 To ensure that these characteristics are satisfied, the individual gratings in the multiplexed holograms are designed to have a volume $Q$ parameter of $Q=\frac{2\pi \lambda d}{n{\mathrm{\Lambda }}^2}\ge 10$, where $\mathrm{\Lambda }$ is the period of the volume grating, $\lambda$ is the reconstruction wavelength, $d$ is the thickness of the hologram, and $n$ is the index of refraction.³⁹ The hologram was fabricated in $d=1.8\mathrm{mm}$ thick phenanthraquinone-doped poly methacrylate (PQ-PMMA), with a measured index of refraction of $n=1.49$. The grating periods for the surface and depth holograms are ${\mathrm{\Lambda }}_{\text{surface}}=4586\mathrm{nm}$ and ${\mathrm{\Lambda }}_{\text{depth}}=4760\mathrm{nm}$ and have $Q$ parameters of 23817 and 22110. Since these values are well above the $Q\ge 10$ condition, volume holograms can be modeled using approximate coupled wave theory as described by Kogelnik.³⁹

The resulting holograms have high diffraction efficiency, $\eta$, in a single diffraction order and high angular and wavelength selectivity. The diffraction efficiency for volume phase transmission holograms sed in the VHI system is given by $\eta =\frac{{\sin }^2{({\nu }^2+{\xi }^2)}^{\frac{1}{2}}}{(1+\frac{{\xi }^2}{{\nu }^2})}$ (with $\nu =\frac{\pi n_{1}d}{\lambda c_r{c}_s};\xi =\frac{\vartheta d}{2c_s}$).³⁹ In these equations, $c_r=\cos ({\theta }_r)$ and $c_s=\cos ({\theta }_s)$, where ${\theta }_r$ and ${\theta }_s$ are the reconstruction and diffracted beam angles, respectively. The hologram angular and wavelength selectivity are determined from the detuning parameter $\vartheta \approx \frac{2\pi }{\mathrm{\Lambda }}[\mathrm{\Delta }\theta \sin (\varphi -{\theta }_o)-\frac{\mathrm{\Delta }\lambda }{2n\mathrm{\Lambda }}]$, where $\mathrm{\Delta }\theta$ and $\mathrm{\Delta }\lambda$ are the angular and wavelength deviations, respectively, from the hologram Bragg condition that causes the diffraction efficiency to decrease to zero.

The multiplexed volume hologram was fabricated using the system shown in Fig. 4. The object beams are formed by focusing a collimated beam through a microscope objective to form a point source. The microscope objective is translated a distance of $\mathrm{\Delta }z$ between each exposure to sample light from a different tissue depth. A collimated reference beam is rotated to a different angle for exposure with each object beam to form a distinct grating within the multiplexed volume hologram.

Fig. 4

Recording geometry of the multiplexed hologram. The recording angle of the object beam, ${\theta }_{\mathrm{obj}}$, is constant at 33.4 deg for both recordings. The reference beam angle, ${\theta }_{\mathrm{ref}}$, changes between 34.92 deg and 31.88 deg for the surface and depth, respectively.

The holograms were recorded with an Argon laser (Coherent Innova 300) at a wavelength of 514 nm and designed to operate at a wavelength of 660 nm light with an inter beam angle of 90 deg between the object and reference beams.⁴¹ The angles for object and reference beams with 514.5 nm light are determined from the $K$-vector or Bragg matching relation: $\overrightarrow{K}={\overrightarrow{k}}_{\mathrm{ref}}-{\overrightarrow{k}}_{\mathrm{obj}}$, where ${\overrightarrow{k}}_{\mathrm{ref}}$ and ${\overrightarrow{k}}_{\mathrm{obj}}$ are the reference and object propagation vectors, respectively, and $\overrightarrow{K}$ is the grating vector that has a magnitude of $\frac{2\pi }{\mathrm{\Lambda }}$. The object beams for both the surface and depth channel are at an angle of 33.4 deg in air relative to the normal to the hologram surface. The reference beam angles for the surface and depth channels are 34.92 deg and 31.88 deg, respectively.

Each hologram in the multiplexed element samples light from a different object depth in the tissue sample. For this system, light is sampled at the object surface and $50\mu \mathrm{m}$ below the surface. Both the surface and depth channels are recorded with curved wavefronts that have the total curvature split with equal but opposite directions of curvature for the two imaging depths. This recording configuration allows for the $50\text{-}\mu \mathrm{m}$ separation, $\mathrm{\Delta }z$, to be balanced between the two channels and provides equal amounts of induced hologram aberration that results from the difference between the recording and reconstruction wavelength (e.g., 514.5 nm for recording and 660 nm for reconstruction). The measured diffraction efficiencies for the multiplexed holographic elements, tested with 633-nm laser light, are 42% and 50% for the surface and depth holograms, respectively. The angular selectivity of the holograms is $\mathrm{\Delta }\theta$ $\sim 0.02\mathrm{deg}$, and the wavelength selectivity, $\mathrm{\Delta }\lambda <0.4\mathrm{nm}$. Each hologram in the multiplexed element diffracts light at two angles separated by $\mathrm{\Delta }\mathrm{\Omega }=34.92\mathrm{deg}$ to $31.88\mathrm{deg}=3.04\mathrm{deg}$ which are then collected by a camera lens (Thorlabs AC254-050). The lens images the diffracted light from each depth to the two rectangular areas at the camera plane. The surface and depth images each occupy half of the camera aperture ($3.39\times 5.43\mathrm{mm}$), corresponding to an FOV of $390\mu \mathrm{m}\times 244\mu \mathrm{m}$ after taking into account the system magnification of 13.9. A SolidWorks rendering of the handle system is shown in Fig. 5.

Fig. 5

SolidWorks rendering of handle component layout. (a) Top-down view demonstrating the layout of the lenses, hologram, and camera; (b) an isometric view indicating the location of the illumination path through the pellicle beam splitter cube.

3.3.

Light Source

The illumination for the system is provided by a 660-nm light-emitting diode (LED) with a full width half max spectral bandwidth of 20 nm. The VHI method is not as susceptible to speckle degradation as other methods such as OCT because VHI does not rely on sensing the coherent interference effects of the detected signal but instead simultaneously projects an image across many pixels of a camera aperture.^42,43 The LED is coupled into a $600\mu \mathrm{m}$, $\mathrm{NA}=0.39$ core fiber (Thorlabs M29L05), which carries the light from the source box to the handle setup, as shown in Fig. 6. To achieve Köhler style illumination, a 10-mm focal length asphere (Thorlabs ACL1210) and a 50-mm achromat (Thorlabs AC127-050-A) are placed after the fiber output to expand the beam to a size of 4 mm to match the microscope objective pupil. The source is placed into the main beam path using a pellicle beam splitter component with 50:50 R/T at 635 nm (Thorlabs CM1-BP150). With this setup, light exiting the microscope objective and entering the endoscope assembly has a planar wavefront in a common path configuration to simplify the design.

Fig. 6

Illumination diagram showing the LED-fiber coupling and the fiber-lens coupling setup representing the expansion of the fiber to fill the microscope objective pupil.